On the convergence of the block nonlinear Gauss-Seidel method under convex constraints

Authors:
L. Grippo;M. Sciandrone
Affiliations:
Dipartimento di Informatica e Sistemistica, Universití di Roma "La Sapienza", Via Buonarroti 12-00185 Roma, Italy;Istituto di Analisi dei Sistemi ed Informatica del CNR, Viale Manzoni 30-00185 Roma, Italy
Venue:
Operations Research Letters
Year:
2000

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Abstract

We give new convergence results for the block Gauss-Seidel method for problems where the feasible set is the Cartesian product of m closed convex sets, under the assumption that the sequence generated by the method has limit points. We show that the method is globally convergent for m=2 and that for m2 convergence can be established both when the objective function f is componentwise strictly quasiconvex with respect to m-2 components and when f is pseudoconvex. Finally, we consider a proximal point modification of the method and we state convergence results without any convexity assumption on the objective function.